How are Artificial Neural Networks and the Biological Neural Networks similar and different?
We all know that artificial neural networks (ANNs) are inspired by but most of them are only loosely based on the biological neural networks (BNNs).
We can analyze the differences and similarities between ANNs and BNNs in terms of the following components.
Neurons
The following diagram illustrates a biological neuron (screenshot of an image from this book).

The following one illustrates a typical artificial neuron of an ANN (screenshot of figure 1.14 of this book).

Initialization
In the case of an ANN, the initial state and weights are assigned randomly. While for BNNs, the strengths of connections between neurons and the structure of connections don't start as random. The initial state is genetically derived and is the byproduct of evolution.
Learning
In BNN, learning comes from the interconnections between myriad neurons in the brain. These interconnections change configuration when the brain experiences new stimuli. The changes result in new connections, strengthening of existing connections, and removal of old and unused ones.
ANNs are trained from scratch usually using a fixed topology (remember topology changes in case of BNNs), although the topology of ANN can also change (for example, take a look at NEAT or some continual learning techniques), which depends on the problem being solved. The weights of an ANN are randomly initialized and adjusted via an optimization algorithm.
Number of neurons
Another difference (although this difference is always smaller) is in the number of neurons in the network. A typical ANN consists of hundreds, thousands, millions, and, in some exceptional (e.g. GPT-3), billions of neurons. The BNN of the human brain consists of billions. This number varies from animal to animal.
Further reading
You can find more information here or here.